Question: Simplify the following expression: $\dfrac{2z^4}{8z^4}$ You can assume $z \neq 0$.
$ \dfrac{2z^4}{8z^4} = \dfrac{2}{8} \cdot \dfrac{z^4}{z^4} $ To simplify $\frac{2}{8}$ , find the greatest common factor (GCD) of $2$ and $8$ $2 = 2$ $8 = 2 \cdot 2 \cdot 2$ $ \mbox{GCD}(2, 8) = 2 $ $ \dfrac{2}{8} \cdot \dfrac{z^4}{z^4} = \dfrac{2 \cdot 1}{2 \cdot 4} \cdot \dfrac{z^4}{z^4} $ $\phantom{ \dfrac{2}{8} \cdot \dfrac{4}{4}} = \dfrac{1}{4} \cdot \dfrac{z^4}{z^4} $ $ \dfrac{z^4}{z^4} = \dfrac{z \cdot z \cdot z \cdot z}{z \cdot z \cdot z \cdot z} = 1 $ $ \dfrac{1}{4} \cdot 1 = \dfrac{1}{4} $